Magnetic resonance imaging (MRI) is now an important imaging technique in medicine. There are described herein several MRI methods using adiabatic excitation. One method accomplishes slice selection with gradient modulated adiabatic excitation. Another method employs slice selection with adiabatic excitation despite large variations in B.sub.1 magnitude. There is also described .sup.1 H spectroscopy using solvent suppressive adiabatic pulses. The methods described herein relate to the adiabatic pulses and methods described in U.S. patent application Ser. No. 032,059, entitled "Amplitude and Frequency/Phase Modulated Pulses to Achieve Plane Rotations of Nuclear, Spin Magnetization Vectors, with Inhomogeneous B.sub.1 Fields", the entire disclosure of which is hereby incorporated by reference herein.